2012 Cambridge Business & Economics Conference
ISBN : 9780974211428
A Simulation Model To Forecast Future Cash-Flows – A Financial Risk
Management Tool
Ralf Bernsau
Karlsruhe Institute of Technology (KIT)
Institute of Applied Informatics and Formal Description Methods (AIFB)
Karlsruhe, Germany
+49 176 32189761
Ralf.Bernsau@student.kit.edu
Andreas Vogel
Karlsruhe Institute of Technology (KIT)
Institute of Applied Informatics and Formal Description Methods (AIFB)
Karlsruhe, Germany
+49 721 60845393
andreas.vogel@kit.edu
Detlef Seese
Karlsruhe Institute of Technology (KIT)
Institute of Applied Informatics and Formal Description Methods (AIFB)
Karlsruhe, Germany
+49 721 60846037
detlef.seese@kit.edu
June 27-28, 2012
Cambridge, UK
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2012 Cambridge Business & Economics Conference
ISBN : 9780974211428
A Simulation Model To Forecast Future Cash-Flows – A Financial Risk Management
Tool
ABSTRACT
This article describes a simulation model which enables the user to forecast the possible
trend of the companies’ Cash-Flow based on historical data, individual estimations,
multivariate regression and the Value-at-Risk concept. The simulation model is able to
simulate Cash-Flows for different individual scenarios and serves due to that as a financial
risk management tool. One interesting feature is that the model uses not just time series of the
relevant market parameters, the multivariate regression includes an additional extern
parameter. This parameter describes the influence of the environment on the future price
trends of the relevant market parameters. The implementation of the extern parameter follows
a random walk. Therefore, the model is not just focusing on a small number of main market
parameters, it also captures the development around these main parameters in one single
factor.
INTRODUCTION
The competition conditions for the manufacturing industry have changed considerably in
recent years. Due to the increasing globalization and the simultaneous fluctuations in
international financial markets, companies face new challenges. As a result of the stronger
integration of the economy and the consequent increase in volatility of commodity prices,
equities, interest and exchange rates, the financial risks of companies have increased.
Especially the recent past confirms that extreme market fluctuations occur at shorter time
intervals and as a consequence the financial position and stability of banks, industrial and
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commercial companies and even of nations is constantly challenged. The financial risk
management is therefore an operational function which importance is increasing more and
more. The success or failure of companies in a challenging environment is essential for their
existence and global competitiveness.
Established on these facts, a lot of companies and academics, such as the National
Economic Research Association (NERA) with the cooperation of the Harvard professor
Jeremy Stein (2000) or the RiskMetrics Group by Alvin J. Lee (1999), developed several
Financial Risk Management Tools to simulate future price trends of stocks, commodities,
interest and exchange rates and so forth. However, the opinions and approaches of these
academics and professionals differ. That’s why Jan Duch (2006) subdivides the different
approaches in two groups. One group is called the Top-Down approach and the other group is
called the Bottom-Up approach.
According to Jan Duch (2006) the aim of the Bottom-Up approach is to make a statement
about the probability that a certain future Cash-Flow adopts a specific value due to the
influencing factors. Attributed to the required knowledge of the business-related effect
relationships, the approaches are called internal models. Additionally, the approach is closely
based on the Value-at-Risk concept. Therefore, it is necessary to implement these models to
start with searching and identifying market-price-based risk factors, which have a significant
impact on the Cash-Flow. Ongoing, the identified financial risks are analyzed by using the
exposure maps according to their importance for the outcome. After that the identified risks
are brought into a functional relationship to simulate the future Cash-Flows. Finally, the
calculation of the Cash-Flow-at-Risk is realized with a user-specific confidence level. On one
hand, Chris Turner (1996) emphasized that the Bottom-Up approach is simple in the way of
the intuitive interpretation of the result. It returns a value, which is exceeded with a given
probability. In addition, it is possible to specify the risk of the probability of deviation from an
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expected value or a quasi-reliable Cash-Flow. On the other hand, Turner states that the
Bottom-Up models can be very complex. The calculation depends very much on the interplay
of the various influencing factors. It is necessary to compute correlations between the
individual parameters, which means that a big data base of time series has to be available.
Furthermore, according to Turner (1996) you have to take in consideration how well the
identified risk factors explain the Cash-Flow. A couple of various different methods are
available to forecast future market prices. One method, which is analyzed by J. Kim, A. Malz
and J. Mina (1999), is based on implied volatilities for short time periods by using
deterministic forward prices. Moreover, according to Lee (1999) a simulation with a random
walk can be implemented, based on historical moments of the distribution of the influencing
factors. Finally, Lee (1999) of the RiskMetrics Group presented an estimation of the CashFlow development by using econometric methods with a so-called Vector Error Correction
Model (VECM).
The perspective of the Bottom-Up approach is not undisputed, because of the many
interdependencies in terms of complexity. Stein (2000) emphasized that the danger might be
large, to observe measurable risks, but easily to ignore other non-financial risks. Unlike the
Bottom-Up approaches, the Top-Down approaches don’t consider separate individual risk
factors. The first Top-Down approaches are the regression models and introduced by Bartram
(1999). The regression models put the Cash-Flow in direct focus. Thus a study of individual
or even entire risk exposures is also possible for non-company employees. The basis is the use
of exclusively public capital market data. Therefore, based on Bartram the regression models
are also called external regression models. The estimation of the volatility of the Cash-Flows
is based on historical deviations. Through this procedure all risks, not only financial, also
operational influences are taken into account, mentioned Stein (2000). Internal Cash-Flow
data is either not available or it is in insufficient amount. Therefore, to explain the variation,
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the models resort to regression analysis for example, with the stock returns or various capital
market data. Another Top-Down model is the benchmark model, which estimates on
historical Cash-Flow distributions and even to some extents from Cash-Flow distribution of
competing companies, the variations. This benchmark model was developed by U.S.
companies. The goal of this approach is to picture a company-wide aggregate risk, without
using individual market parameters as the previous models. Simply put, it compares historical
Cash-Flows from other companies in the same sectors with the company looked at, and then
draws conclusions about possible future Cash-Flow trends. Therefore, no detailed knowledge
is required about internal relationships in order to make a statement about the risk exposure of
the company. The consulting firm National Economic Research Associates (NERA) from
New York developed in 2000 such a model called C-FAR, where C-FAR stands for CashFlow-at-Risk. Like the two previous simulation models this model is also based on historical
Cash-Flow time series. Although Stein (2000) highlighted in his paper, that the general
problem is, that there are not enough empirical Cash-Flows existing, especially due to
changes in corporate structure or company size.
The model, which will be explained in this article, belongs to the Bottom-Up approach.
The aim of that developed and implemented model is to anticipate future market movements
and to measure the hazard on company’s financial strength and stability. The model is able to
consider many single factors, which directly or indirectly influence the company’s wealth and
economic strength. As a model stays always a model and can never predict the future with
absolute certainty, nevertheless it is fundamental for global and international as well as
national active companies to manage their risks. The model gives a good indication on
possible future situations and simulates different economical scenarios. The company using
the modeli will be able to deal with their risk and to get a better overview about coherences,
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market factors and the consequences of their movements to evaluate the simulated world
against reality.
The model uses regression analysis and historical time series. However, none of the
outlined models are able to describe the development of the environment and include the
trend in the prediction of future prices.
The article starts with explanations and descriptions of our simulation model and will
continue with providing analyses and the evaluation of the model. The summary will
conclude the described explanations and analyses of our simulation model.
THE MODEL
Portfolio optimization is primarily understood as the ability to simulate and evaluate a
combination of several products. For economic reasons, it is realistic that a company produces
and sells several products. Every company is able in our model to produce multiple products
with different features. On one hand, the company has to determine for each product in its
portfolio, the income elasticity and price elasticityii. On the other hand, a product-based
allocation of sales, the expected value and standard deviation of the sales need to be indicated.
Furthermore, each product is assigned a price, which is ideally above the production costs in
order to realize a profit margin. Finally, each product must be assigned a breakdown in
percentage proportion of the raw materials required. Through that, different products can be
simulated with different features.
Through the implementation of the individual products, the total sales of a company
results from the sum of the sales of the individual products. The single turnovers arise from
the sales of the products in Germany. The price of each product develops analogous to the
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Consumer Price Index (CPI) and automatically adjusts to the corresponding demand. Thus,
the formula to show the price trend is:
𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑃𝑟𝑖𝑐𝑒𝑥,𝑡 = 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑃𝑟𝑖𝑐𝑒𝑥,𝑡−1 ∗
𝐶𝑃𝐼𝑡
𝐶𝑃𝐼𝑡−1
(1)
with 𝑥: 𝑃𝑟𝑜𝑑𝑢𝑐𝑡
The turnover itself is derived from the sales of the previous period multiplied by the
domestically economic development, the gross domestic product (GDP), is due to the income
elasticity of demand. In addition, the turnover is influenced by the pricing of the product and
weighted by the price elasticity. Alike the model considers diverse volatilities in sales, which
can occur due to production, demand or external reasons. Fluctuations in production may
arise for example, through line stoppage, staff absences or raw material supplies. This
fluctuation is realized through the generation of a normally distributed random variable using
the polar method of George Marsagliaiii. Thus, the calculation of product-specific sales results
from the formula:
𝑆𝑎𝑙𝑒𝑠𝑥,𝑡 = 𝑆𝑎𝑙𝑒𝑠𝑥,𝑡−1 ∗ [1 + (
𝐺𝐷𝑃𝑡
− 1) ∗ 𝜖𝑥,𝑒 ]
𝐺𝐷𝑃𝑡−1
(2)
𝐶𝑃𝐼𝑡
− 1) ∗ 𝜖𝑥,𝑝 ]
𝐶𝑃𝐼𝑡−1
∗ [1 + 𝑅𝑎𝑛𝑑𝑜𝑚 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒(𝜇, 𝜎)]
∗ [1 + (
with 𝑥:
𝜖𝑥,𝑒 :
𝜖𝑥,𝑝 :
𝜇:
𝜎:
𝑃𝑟𝑜𝑑𝑢𝑐𝑡
𝐼𝑛𝑐𝑜𝑚𝑒 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑥
𝑃𝑟𝑖𝑐𝑒 𝑒𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑥
𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑎𝑙𝑒𝑠
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑠𝑎𝑙𝑒𝑠
The company also incurred product-specific costs, which are explained in terms of
material costs. As already mentioned, each commodity is traded in US-Dollar. Furthermore,
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we make the assumption that the storage is refilled with raw materials at the beginning of
each quarter to keep the storage constant. It will be bought just as much material as is required
in order to realize the simulated sales. Thus, the product-specific material costs result from the
sum of the portions of each commodity multiplied by its price and then adjusted for the
𝐸𝑈𝑅
𝑈𝑆𝐷
-
exchange rate.
𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝐶𝑜𝑠𝑡𝑠 𝑝𝑒𝑟 𝑈𝑛𝑖𝑡𝑥,𝑡
𝑈𝑆𝐷
∑𝑛𝑖=1 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑖 ∗ 𝑃𝑟𝑖𝑐𝑒𝑖,𝑡 (
𝑇𝑜𝑛𝑠)
=
𝐸𝑈𝑅
𝐸𝑥𝑐ℎ𝑎𝑛𝑔𝑒 𝑅𝑎𝑡𝑒𝑡 (𝑈𝑆𝐷 )
(3)
with 𝑥: 𝑃𝑟𝑜𝑑𝑢𝑐𝑡
𝑖: 𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 (𝐶𝑜𝑚𝑚𝑜𝑑𝑖𝑡𝑖𝑒𝑠)
The three above derived formulas are taken together and described as a so-called
exposure map. This exposure map is individually constructible for each product of a
company. For consideration of the overall risk, the risk potential of the various influencing
factors or market parameters on the Cash-Flows needs to be identified. To use the Cash-Flowat-Risk it is necessary to determine the sensitivity to changes in the considered market
parameters and for these circumstances the exposure map is used. According to Duch (2006)
the exposure map is an economic mapping, which derives its focus on changes for the
company's profit, due to changes in the revenue . Thus, the Cash-Flow for a product results by
using the formula:
𝐶𝐹𝑥,𝑡 = (𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑃𝑟𝑖𝑐𝑒𝑥,𝑡 − 𝑀𝑎𝑡𝑒𝑟𝑖𝑎𝑙 𝐶𝑜𝑠𝑡𝑠𝑥,𝑡 ) ∗ 𝑆𝑎𝑙𝑒𝑠𝑥,𝑡
(4)
with 𝑥: 𝑃𝑟𝑜𝑑𝑢𝑐𝑡
Through the consideration of multiple products it is necessary, to calculate the total
turnover of the company in a quarter, to add up the individual product-specific Cash-Flows.
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𝑥
(5)
𝑂𝐶𝐹𝑡 = ∑ 𝐶𝐹𝑥,𝑡
𝑥=1
with 𝐶𝐹𝑥,𝑡 : 𝐶𝑎𝑠ℎ − 𝐹𝑙𝑜𝑤 𝑓𝑜𝑟 𝑃𝑟𝑜𝑑𝑢𝑐𝑡 𝑥
The five mentioned formulas are the base to calculate the Cash-Flows of a company. As
outlined in the preparation of the exposure maps, we identified four key market parametersiv,
which are essential to simulate the future Cash-Flows of an industrial enterprise. There is the
gross domestic product (GDP) of the Federal Republic of Germany, the consumer price index
(CPI), the long-term interest rate EURIBOR and the
𝐸𝑈𝑅
𝑈𝑆𝐷
- exchange rate.
The gross domestic product (GDP) reflects directly the added value of the observed
economy in the corresponding quarter. However, the problem with this measure is the
frequency of data collection. Therefore to achieve a high statistical reliability, it is necessary
to use a relatively long observation period of the past. Nevertheless, the quarterly GDP
represents the key indicator for the quantification of the economy. In addition, we use
seasonally and calendar adjusted values of the GDP, which the Federal Statistical Office of
Germanyv makes available to avoid distortions of the actual economic development by
seasonal influencesvi . By stating to the quarterly values in determining the economy, all other
parameters need to be stated to quarterly values as well. This raises the fundamental question,
whether we rely on average values of the quarters, or on a daily rate during the quarter.
According to Siebert (2010) a calculation of quarterly averages distorts the actual volatility of
the price developments, that’s why we use the closing price of the last trading day of each
quarter.
The next key indicator is the exchange rate. Based on the quarterly data supply of the
GDP, the exchange rate will also be evaluated at the end of every quarter. The euro reference
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rates of the European Central Bank (ECB) deliver the needed data of the
ISBN : 9780974211428
𝐸𝑈𝑅
𝑈𝑆𝐷
- exchange rate.
These euro reference rates are determined and published each business day through the
participation of the European Central Bank and the National Central Banks and reflect the
market price of the euro against major international currencies, stated Siebert (2010). The data
series for the euro reference rates are accessible on the website of the German National
Bankvii .
It is also for the interest rate necessary to find a reference price, which reflects the general
interest rate trends. Here arises the problem that, unlike the exchange rate many differing
interest rates, for which banks lend money, are available. An appropriate index for the interest
rate development is the Euro Interbank Offered Rate (EURIBOR). The EURIBOR is a
reference rate, calculated by the ECB for time deposits in the interbank marketviii . This rate
refers, in contrast to existing competition interest rates, such as the London Interbank Offered
Rate (LIBOR), exclusively on the Euroix . Since the EURIBOR is calculated at different
maturities and serves as a reference rate for floating rate notes and swaps, its use provides the
representation for our interest rate. To map the corresponding long-term interest rates we
chose the EURIBOR with the longest duration, twelve months. The historic EURIBOR time
series are available on the website of the German National Bank. Like the GDP we use for the
interest rate the quarterly value of the daily closing price of the last trading day of each
quarter.
As part of this market model we made the assumption that changes in commodity prices
develop in line with prices in the economy. Against this background, the consumer price
index (CPI), which is determined monthly by the Federal Statistical Office of Germany, is an
accurate measure of consumer prices based on the Laspeyres price indexx. The CPI is used as
a benchmark in wage negotiations and is constituted as the central indicator for the
assessment of monetary developments in Germany. Furthermore, the changes in the consumer
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price index or its internationally adapted form, called the harmonized consumer price index,
are a measure of inflation in Germany. As we saw with the GDP, is it also necessary for the
CPI to use seasonally and calendar adjusted values to avoid distortions of the actual
development. Therefore, like Siebert (2010) we also used the value of the CPI of the last
month of each quarter during the considered time period.
Once the metrics are defined to quantify the key market parameters, the influences among
the parameters need to be estimated. This turns out to be difficult, because on the theoretically
profound basis you can find out, which factors affect another factor. The problem is that you
cannot make precise statements about the strength and delay of the influence. Like the
conventional risk models, the forecasts of the market parameters are calculated from returns.
According to that, the influence of a parameter on another parameter is not based on the
absolute value but on the return. The relevant relations of the derived market parameters were
determined by using the theoretical principles. In addition, we used the t-statistics and the
analysis of the correlations based on time series, for supporting the given theoretical relations.
The correlation of two time series measures the significance of the direct influence of the
return of a market parameter in t-1 on the return of a market parameter in t. The t-statistics
measures the goodness of the gradient of the correlation and therefore rejects or supports the
observed theoretical principles and estimated correlations of the market parameters. The news
service Bloomberg provides the needed time series of the various market parameters. Beyond
that, we used time series from the first quarter of 1990 to the second quarter of 2011, to
provide a solid base of data to estimate influences and correlations between the market
parameters. For example, we assessed a direct influence of the exchange rate on the long-term
interest rate. The theory implies that expectations about the future exchange rate have a direct
impact on net foreign investments. These net foreign investments arise from the difference
between investments of residents abroad and of domestic investments of foreigners. In
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absence of arbitrage the expectation of a re-valuation of the domestic currency leads to a
higher demand for domestic bonds. Through that context, the domestic interest rate falls and
the price of bonds rises. On the other hand, it is an expectation of a devaluation of domestic
currency. As a result, the investment in foreign money is attractive. This leads to an outflow
of capital to foreign countries. The reason for this observation is, that foreigners are now
investing in their own country and nationals in the foreign country, based on the higher
expected returns in the foreign country. Therefore, the net foreign investments decrease and
the demand of domestic bonds regresses, whereby the interest rate raisesxi. As a result of this a
connection between the development of the exchange rate and the development of the interest
rate is supposed. Additionally, the estimated correlation of the time series of the exchange rate
and the interest rate is supported by the t-statistics and therefore the estimated direct influence
cannot be statistically rejected.
We determined direct influences between the four key indicators and moreover a
relationship to the individual raw materials. The direct influences between all the relevant
market parameters are shown in table 1. The letter X implies a direct influence. The raw
materials we used to simulate different products in our fictive simulation are aluminium
(Alu.), copper, nickel and zinc. The times series of the four mentioned raw materials are also
provided by Bloomberg and are based on the time period of 1990 to 2011.
Once we evaluated all the relevant effect relationships between the relevant market
parameters, we define now a regression analysis, which will be implemented and applied at a
later point to give these relationships a real number in the context of a coefficient. The
primary scope of the regression analysis is the investigation of causal relationships, or the socalled cause-and-effect relationships. In the simplest case, such a relationship can be
expressed between two variables, the dependent variable Y and the independent variables X.
The variables X and Y always correspond to the respective returns of a market parameter,
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which can be determined in the simulation model. The multivariate regression approach has
the following formxii :
𝑌̂𝑗 = 𝑎0 + 𝑎1 ∗ 𝑥1 + 𝑎2 ∗ 𝑥2 + … + 𝑎𝑖 ∗ 𝑥𝑖 + 𝑒𝑘
with 𝑗:
𝑌̂𝑗 :
𝑎0 :
𝑎𝑖 :
𝑥𝑖 :
𝑒𝑘 :
(6)
𝐷𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 𝑌 − 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟
𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒
𝑅𝑒𝑔𝑟𝑒𝑠𝑠𝑖𝑜𝑛 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑀𝑎𝑟𝑘𝑒𝑡 𝑃𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠 𝑖
𝐼𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 − 𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟
𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒
It consists of the sum of the individual influencing market parameters, together with
respective regression coefficients. Due to the fact, that between the regression line and the
observed values deviations exist, it can be assumed, that there is no straight line on which all
the observed (x, y) – combinations belong to. The consulted market parameters are not
sufficient to describe the entire process of a specific market parameter. The influencing
variables which are not covered of the empirical Y- values are reflected in very low deviations
from the regression line. These deviations can be represented by a vector 𝑒, whose values 𝑒𝑘
is known as residuals. Thus, Y is additively from its systematic components, the identified
influencing factors and the residual 𝑒𝑘 . The regression coefficients 𝑎𝑖 have an important
substantive meaning, they indicate the marginal effect of the change of an independent
variable on the dependent variable Y. The quantity of the regression coefficients should not
be regarded as a measure of the importance of that variable. The calculation of the regression
coefficients 𝑎𝑖 is based on the minimization of the sum of squared residuals.
Once all regression coefficients are calculated, it is now necessary to determine the
environmental influence. In the multivariate regression model, it is not possible to integrate
directly the environment, because there are no empirical variables and returns of the
development of the environment. The special feature of this simulation model is exactly the
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basis of our approach, we determine the environmental factors as well as its impact. Based on
that, we imply the unexplained portion in the regression function as an influence with a
regression coefficient and a variable. To realize this approach, we use the multiple
determination 𝑅 2 . The multiple coefficient of determination is a global quality measure,
which indicates how well the dependent variable is explained by the regression model. The
basis are the calculated residuals. In order to assess these residuals, we need a benchmark.
This benchmark is calculated as the difference between the observations 𝑦𝑘 and the mean 𝑦̅.
Furthermore, it requires the scattering decomposition based on the total sum of squared
deviationsxiii. Thus, follows the calculation of the multiple coefficient of determination the
equation:
𝑅2 =
∑𝐾
̂𝑘 − 𝑦̅)²
𝐷𝑒𝑐𝑙𝑎𝑟𝑒𝑑 𝑆𝑝𝑟𝑒𝑎𝑑
𝑘=1(𝑦
=
𝐾
∑𝑘=1(𝑦𝑘 − 𝑦̅)²
𝑇𝑜𝑡𝑎𝑙 𝑆𝑝𝑟𝑒𝑎𝑑
with 𝑅 2 :
𝑦𝑘 :
𝑦̂𝑘 :
𝑦̅:
𝐾:
(7)
𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛
𝑉𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠
𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑌 𝑓𝑜𝑟 𝑥𝑘
𝑀𝑒𝑎𝑛
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛𝑠 (𝑘 = 1,2, . . , 𝐾)
The multiple coefficient of determination is a normalized value and represents values in
the interval [0,1]. The greater the proportion of the explained variation to total variation is, the
greater is the value of 𝑅 2 . The coefficient of determination can be determined as the square of
the correlation. However, in the multivariate case the estimated variables must be formed by
linear combinations of several independent variables. Therefore, 𝑅 refers to a multiple
correlation coefficients. By considering the environment with the multivariate regression
model, we assume a bivariate context. According to this, the relationship can be expressed as:
𝜌𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 = √1 − 𝑅 2
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(8)
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with 𝑅 2 :
𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝑜𝑓 𝐷𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑡𝑖𝑜𝑛
𝜌𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 : 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑡ℎ𝑒 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡
𝑎𝑛𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑗
The formula approximates the correlation of the environment with the respective
multivariate regression model of each market parameter. The determined correlations are now
the basis for the derivation of the influences and regression coefficients for the environment.
However, one should bear in mind, that this is an approximation to the actual value.
To determine the influence coefficients 𝑎𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 , we have to adjust the calculated
correlation with the standard deviation of the environment and the relevant market parameter.
Thus, the formula for calculating the influence of an exogenous variable on a market
parameter isxiv.
𝑎𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 = 𝜌𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 ∗
𝜎𝑗
(9)
𝜎𝑒𝑥𝑡𝑒𝑟𝑛
with 𝜎𝑗 :
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑡ℎ𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑗
𝜎𝑒𝑥𝑡𝑒𝑟𝑛 : 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 𝑡ℎ𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑣𝑖𝑟𝑜𝑚𝑒𝑛𝑡
𝜌𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 : 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑣𝑖𝑟𝑜𝑚𝑒𝑛𝑡 𝑤𝑖𝑡ℎ 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑗
Because the environment returns are constructed as random numbers, the choice of the
standard deviation is arbitrary. In this context, the standard deviation of the environment
returns is set at one percent and the influence coefficients 𝑎𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 are calculated according to
equation 9. Regarding the expectation values of the normally distributed environment returns,
the historical arithmetic average values of the corresponding market parameters shall be
considered, to reflect the historical trend of the market. For example, the chosen economic
indicator GDP, generally shows an empirical rising trend, which justifies the use of this trend.
For the final determination of the expectation value 𝜇 of the environment return we used the
previously determined influence coefficients. According to Siebert (2010) the expectation
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value of the environment return has to be chosen in that way, that it explains the given
expected development of a market parameter, which cannot be completely described by the
considered influencing factors. As soon as we simulate different scenarios, we assume an
expected trend of a market parameter, and due to that the environment return will be adjusted
to that trend. If we don’t consider an individual trend for a specific market parameter, we
determine the expectation value of the environment return through the historical market
average of the corresponding parameter and the historical averages of the influencing factors.
8
̅̅̅̅̅̅̅̅̅̅
𝑅𝑒𝑡𝑢𝑟𝑛𝑗,𝑡 = 𝑎𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 ∗ 𝜇𝑒𝑥𝑡𝑒𝑟𝑛 𝑗,𝑡−1 + ∑ 𝑎𝑖 ∗ ̅̅̅̅̅̅̅̅̅̅
𝑅𝑒𝑡𝑢𝑟𝑛𝑖,𝑡−1
(10)
𝑖=1
mit
𝑎𝑒𝑥𝑡𝑒𝑟𝑛 :
𝑎𝑖 :
̅̅̅̅̅̅̅̅̅̅
𝑅𝑒𝑡𝑢𝑟𝑛𝑗,𝑡 :
̅̅̅̅̅̅̅̅̅̅
𝑅𝑒𝑡𝑢𝑟𝑛𝑖,−1𝑡 :
𝐼𝑛𝑓𝑙𝑢𝑒𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡 𝑜𝑛 𝑗
𝐼𝑛𝑓𝑙𝑢𝑒𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑖 𝑜𝑛 𝑗
𝑒𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑗 𝑖𝑛 𝑡
𝑒𝑚𝑝𝑖𝑟𝑖𝑐𝑎𝑙 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑖 𝑖𝑛 𝑡 − 1
Due to formula 10, the expectation value of the corresponding environment return can be
determined through the calculated influence coefficients and the historical average values.
Thus, the environment returns are given as normally distributed random numbers with the
standard deviation of one percent and with the expected value 𝜇𝑒𝑥𝑡𝑒𝑟𝑛,𝑗−1. The normal
distributed random values are realized through the polar method of George Marsagliaxv.
Hence, all the basics to calculate the development of the various market parameters are
now given. The implementation results from the sum of the newly estimated regression
coefficients of each market parameter plus the influence of the environment. According to
this, the formula to simulate future returns of each market parameter is given by the weighted
sum of the yield of individual influencing factors and the rate of change of the environment,
which is simulated by generating a random number.
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8
(11)
𝑅𝑒𝑡𝑢𝑟𝑛𝑗,𝑡 = 𝑎𝑒𝑥𝑡𝑒𝑟𝑛,𝑗 ∗ 𝑅𝑒𝑡𝑢𝑟𝑛𝑒𝑥𝑡𝑒𝑟𝑛 𝑗,𝑡−1 + ∑ 𝑎𝑖 ∗ 𝑅𝑒𝑡𝑢𝑟𝑛𝑖,𝑡−1
𝑖=1
mit
𝑎𝑒𝑥𝑡𝑒𝑟𝑛 :
𝑎𝑖 :
𝑅𝑒𝑡𝑢𝑟𝑛𝑖,𝑡−1 :
𝑅𝑒𝑡𝑢𝑟𝑛𝑒𝑥𝑡𝑒𝑟𝑛 𝑗,𝑡−1 :
𝐼𝑛𝑓𝑙𝑢𝑒𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡 𝑜𝑛 𝑗
𝐼𝑛𝑓𝑙𝑢𝑒𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑖 𝑜𝑛 𝑗
𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟𝑠 𝑖 𝑖𝑛 𝑡 − 1
𝑅𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡 𝑓𝑜𝑟 𝑖 𝑖𝑛 𝑡 − 1
On the basis of this multivariate regression analysis, the future price developments of the
individual market parameters are simulated and ongoing the Cash Flows are calculated with
the presented exposure map. Once the simulation model simulated a user-defined time period,
the model returns the Cash-Flow-at-Risk to an expected value of zero or a specified
benchmark.
The model itself has a very flexible character to simulate the regarded world. It’s
individual and company specific and can be expanded and supplemented by other relevant
factors. One suggestion of the model and its application are shown and illustrated in the
following chapter.
EVALUATION
To evaluate our simulation model, it is necessary to back test it. This is done through
stress testing, to estimate how a simulated portfolio of a company responds to extreme
economic conditions.. To do so, we have to follow two steps. First, we develop plausible
scenarios with market fluctuations. Then the evaluation of the portfolio with respect to a
given scenario follows. In this paper, the simulated portfolio includes a maximum of three
different products, which are composed from the given resources of the simulation model.
The three products are presented in the exposure map (table 2) and consist of four different
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raw materials. The raw materials are aluminum, copper, nickel and zinc, which allow to
produce various metal products. These raw materials should constitute the basis of this
analysis. The pricing of a product is based on the partial prices of the raw materials and does
not include any additional fixed costs. The market fluctuations for the stress testing are
generated of the standard deviations and the corresponding expectation values of the market
parameters. Moreover, due to possible variations in sales on the corporate basis, the sales of a
product are controlled by its expected value and volatility. Fluctuations can occur in this
context by machine breakdowns, lacks of production means or technical know-how. In
addition, the company can not sell the goods in foreign countries; otherwise we have to
consider additional exchange rate risks.
The simulation period in all simulated scenarios is 16 quarters or four years. The choice
of the four years is due to the fact, that we consider a short-term cycle in the sense of Kitchin
(1923). The fluctuations in this Kitchin-cycle are caused by the storage and production of
companies, which leads to a reasonable observation period. However, also exogenous effects
can occur, such as wars, natural disasters or financial instability in the world's economies.
The validity of a simulation is thereby strengthened and interpreted as soon as it is
repeated several times. Only by this way it is possible to obtain a distribution of Cash-Flows,
which can be analyzed with the confidence level. To strengthen and to increase the
significance of a scenario we chose as part of the stress tests a number of 5000 simulation
runs. To calculate the Cash-Flow-at-Risk to a expected value of zero, we determined for all
scenarios a confidence level of 95 %. This means that with a probability of 95 % the future
Cash-Flows exceed the calculated Cash-Flow-at-Risk.
Once all required parameters are specified, the implementation of the various scenarios
follows. Subsequently the generated Cash-Flow distributions are analyzed by using
theoretical fundamentals and charts.
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Standard and 20 % Volatility: In the first two scenarios, we consider the portfolios
with three different products. The layout of the products can be found in table 2. The first
scenario Standard uses the obtained average returns, correlations and regression coefficients
of the historical time series, to simulate future prices. In the second scenario Vola_20%, all
implied volatilities of all market parameters are increased by 20 %. This test is intended to
help analyzing how the model behaves with strong market fluctuations of all market
parameters.
The results of the simulations are shown in Figure 1. The Cash-Flow-at-Risk of scenario
Standard is less than the Cash-Flow-at-Risk for the scenario Vola_20%.
Furthermore, by increasing the volatility of each market parameter, the volatility of the
Cash-Flow distribution is higher. This observation fulfills the expectation. The variation in the
volatility of a market parameter describes the direct influence of the environment on the
current market parameter. With an increased volatility, the influence of the environment is
greater (Equation 9). The development of the environment is not predictable, because based
on the Polar-method the future development is generated by a random walk. Therefore, the
results show a possible plausible development at a higher volatility of the market parameters.
The small deviation between the Cash-Flow-at-Risk results probably stems from the fact that
the general development of the simulation model suggests a growing economy and thus an
increase in sales. Based on the assumption that the historical time series imply a positive
development of the economy and consumption, the distribution of the Standard scenario also
seems to be plausible. The products and in particular the prices of the products are conceived
in that way that in any case, the prices cover the variable costs and so have a positive CashFlow.
Challenging economic conditions: So far we simulated a scenario based on historical
time series and one scenario with an increased volatility of 20 %. However, the observation of
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extreme market volatility is of particular interest in the evaluation of the simulation model.
Therefore, we simulated in the following section, three scenarios that will test the simulation
model at extreme negative developments. The first scenario BIPnull reflects a prolonged
recession with no growth in the economy. The second scenario is MetalsUp which simulates
the impact on the Cash-Flow by using two times the expected price increase of the raw
materials. This scenario for example could arise by an increasing demand of metals from
developing countries.
The third scenario MetalsUp_SalesDown exacerbates the previous scenario by falling
sales of all three products by 20 % caused by internal conditions. Here machine breakdowns
or material defects may be responsible for a falling rate of production. The distributions of the
simulated scenarios are shown in Figure 2. The Cash-Flow-at-Risk results of each scenario
show, that with rising prices of raw materials, the highest probability for a negative outcome
is achieved. However, the lowest mean of the Cash-Flows is achieved by the scenario with
rising metal prices and dropping sales. Therefore, the average of the lowest Cash-Flow is
generated by the third scenario. Moreover, the volatility of the third scenario is significantly
lower and the concentration of the results to a particular sample space is higher. This
concentration results from the simultaneous decrease in the rate of production and the rising
prices. On the one hand, the sales decrease and on the other hand, the costs increase
significantly. The results of the three scenarios seem also to be plausible.
The simulated Cash-Flows with the increased prices for raw materials and the stagnant
economy are significantly lower than the previous scenarios. On the one hand, the production
of products gets more expensive, and thus reduces the profit margin significantly. On the
other hand, through a stagnant economy the sales are hampering and the revenue is
collapsing.
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Booms and economically beneficial scenarios: After we examined negative
developments, which can occur, we are now analyzing economically beneficial scenarios.
There are two different scenarios constructed. These scenarios are based on the exact opposite
trends as the previously considered scenarios. The first scenario implies a recovering
economy as it occurred in the years 2009 and 2010 in Germany. The Federal Statistical Office
of Germany recorded in the 3rd Quarter of 2009 a growth of the gross domestic product of
2.3 %.
Therefore, in the first scenario we assume a growth in gross domestic product of 2.5 %,
which should contribute to increasing sales. The second scenario implies falling metal prices,
which should lead to lower production costs. The prices of raw materials develop exactly
opposite to the average empirical development of the last decades. The distributions of
simulated Cash-Flows are shown in Figure 3. As you can see in the two charts, an economic
upturn has a greater positive influence on the market and the production volume and therefore
on the Cash-Flow development, as falling prices. Falling prices increase the profit margin but
not the sales and thus the revenue.
Comparison of considered business cycles: Finally, we are now comparing the different
results from three different types of scenarios. The goal is to contrast the different
distributions of Cash-Flows. Figure 4 shows the simulated Cash-Flows of the scenarios
Standard, BIPnull and BIPup. In the diagram you can see clearly the differences between the
two extreme scenarios and the standard scenario. The shifts in the Cash-Flow distributions
show that the simulation model is able to generate possible future Cash-Flow developments,
based on the changed market parameters. Figure 5 shows the shift of the Cash-Flows with
falling and rising commodity prices compared to the simulation with the average empirical
development based on historical time series. However, it can be recognized that the shifts of
the distributions to the left and right on the X-axis are lower as in the previous scenarios. This
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means that the impact of falling and rising commodity prices has a smaller impact on the
future Cash-Flow development in comparison to cyclical market fluctuations.
Figure 6 illustrates the Cash-Flow-at-Risk results of each scenario. The diagram shows
that the results are similar for the same respective circumstances. With an increasing
economic activity and falling prices of raw materials, a significantly higher Cash-Flow-atRisk can be determined, in comparison to the standard development and in particular to rising
commodity prices and the sluggish economy.
Furthermore, the difference between an increase in volatility and the simulation with the
average historical development is evident. The Cash-Flow-at-Risk is lower, equally the mean
of the scenario Vola_20%. However, the chart 1 shows that the distributions are very similar.
In scenario Vola_20% you would expect to see the consequences of the higher deviations with
a more significant effect in results in comparison with the Standard scenario. This is not
observable, because the model implicitly takes coherences between market factors into
consideration and that leads to the resulting distribution. The Cash-Flow-at-Risk result for the
scenario MetalsUp is almost zero, that’s why it cannot be seen in the diagram 6. The result is
mapped between the result of the scenarios BIPnull and MetalsUp_SalesDown.
In Table 3 are all the results of the Cash-Flow-at-Risk calculations of each scenario
presented. Like mentioned before, the simulated Cash-Flows aren’t including any fixed costs
the company faces through the production of the products. Through that assumption, the
Cash-Flow-at-Risk results in the following table seem big and aren’t negative or zero for the
scenarios you would expect that. However, the Cash-Flow-at-Risk results of the different
scenarios differ significantly and show that the simulation model works as it was expected.
In summary, we conclude that the simulation model explains the relationships of the
various market parameters well. The generated simulations show that the expected results
occur, and thus the robustness and stability of the model is proved. Even in extreme market
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fluctuations, the simulation model provides reasonable results and does not reject the
calculated correlations.
CONCLUSION
The simulation model is based on System Dynamics, bivariate and multivariate
regression analysis and also on the principle of random walk and the Cash-Flow-at-Risk
approach. This macroeconomic market model is able to simulate and aggregate in the context
of a corporate exposure map and the inclusion of business-relevant market factors, future
Cash-Flows.
The simulation model is capable of simulating different scenarios with different
configurations of the various market parameters. The scenario analysis shows that the model
has the required quality and robustness to deliver plausible results even in extreme market
situations. Moreover, an adaptation of the implementation on other companies is feasible with
relatively little effort, based on the circumstance of the individual configuration. The fact that
the model uses the multivariate regression analysis to measure the direct influence of
individual market parameters on other factors increases the validity and reflects the theoretical
and the empirical correlations in more detail.
The consideration of an exogenous variable which is defined as the environment and the
evaluation of an influence of that variable on the development of the considered market
parameters is in contrast to a lot of other models. However, not only the implication of an
exogenous variable, also the consideration of historical returns to predict the future
development, differs from various models. The use of empirical data is efficient and often the
only possibility for quantifying theoretical relationships. However, the projection of empirical
relationships for the future can lead to incorrect results. Historical data deliver just snapshots
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2012 Cambridge Business & Economics Conference
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of possible developments, which will not recur in the same constellation in the future. That’s
why it is possible that through structural breaks in the context of the market dynamic these
empirical correlations lose their validity. The problem in this context is the low frequency of
data to describe stable relationships.
Starting points for future studies would be in the observation of the nonlinearity of the
regression coefficients. Bartram (1999) describes the non-linearity as the complexity of the
exposure and the difficulty of a correct evaluation of financial risks through the capital
markets. That could lead to small changes in exchange rates, which are superimposed of other
price relevant information. This means that financial market participants consider only large
exchange rate fluctuations in the business valuation or Cash-Flow calculation. In addition, the
use of historical data to forecast future prices is in the literature discussed with controversy.
Above that, the model shows a flexible character with the possibility of implementing further
enhancements. That could be considering default risk within supply or storage costs due to
fluctuation in demand.
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2012 Cambridge Business & Economics Conference
ISBN : 9780974211428
TABLES
t-1\t
GDP
GDP
X
CPI
X
EUR/USD
X
Interest
Alu.
Copper
Nickel
Zinc
CPI
X
X
EUR/USD Interest
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
Alu.
X
X
X
X
Copper
X
X
X
X
Nickel
X
X
X
X
Zinc
X
X
X
X
Table 1: Matrix of the influencing coefficients
Product 1
Income elasticity
Price elasticity
Price
Sales
Sales μ
Sales σ
Aluminium
Copper
Nickel
Zinc
1
-1
1000
3000
0
0
0.2
0.02
0.005
0.005
Product 2 Product 3
0.5
1.2
-1
-1.5
1100
40
3000
15000
0
0
0
0
0.3
0.01
0.02
0.001
0.001
0
0
0
Table 2: Stresstesting Exposure Map
CFaR
Mean of the CF‘s Standard deviation
Standard
30,372,894.69
56,600,668.43
14,475,630.82
Vola_20%
23,184,192.12
56,283,574.33
17,779,785.99
BIPnull
2,417,715.73
35,492,772.54
18,699,541.03
MetalsUp
15,330.14
35,717,172.65
19,902,825.30
MetalsUp_SalesDown 5,068,065.91
17,718,321.23
7,124,585.93
BIPup
87,656,579.66
100,611,857.40
7,234,513.07
MetalsDown
63,029,150.07
79,346,077.07
9,010,692.07
Table 3: Results of the scenarios
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2012 Cambridge Business & Economics Conference
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FIGURES
Figure 1: Standard development and volatility increases by 20%
Figure 2: Sluggish economy, rising commodity prices and sales decline
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2012 Cambridge Business & Economics Conference
ISBN : 9780974211428
Figure 3: Improving economy and falling commodity prices
Figure 4: Comparison of standard development with a stagnating and attractive economy
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2012 Cambridge Business & Economics Conference
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Figure 5: Comparison of standard development with falling and rising commodity prices
Figure 6: Cash-Flow-at-Risk distribution of scenarios
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2012 Cambridge Business & Economics Conference
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REFERENCES
Backhaus, K., & Erichson, B., & Plinke, W., & Weiber, R. (2008). Multivariate
Analysemethoden – Eine anwendungsorientierte Einführung. Berlin: Springer – Verlag
Bartram, S. M. (1999). Corporate Risk Management – Eine empirische Analyse der
finanzwirtschaftlichen Exposures deutscher Industrie- und Handelsunternehmen. Bad
Soden/Ts: Uhlenbruch
Duch, J. (2006). Risikoberichterstattung mit Cash-Flow at Risk-Modellen. Frankfurt am
Main: Lang
Junius, K., & Kater, U., & Meier, C. P., & Müller, H. (2002). Handbuch Europäische
Zentralbank : Beobachtung, Analyse, Prognose. Bad Soden/Ts.: Uhlenbruch
Kim, J., & Malz, A., & Mina, J. (1999). LongRun Technical Document. New York:
RiskMetrics Group
Kitchin, J. (1923). Cycles and Trends in Economic Factors. The Review of Economics and
Statistics, 5(1), 10–16
Lang, C. (2005). Theoretische und empirische Aspekte der Prognose wichtiger
makroökonomischer Größen. Göttingen: Cuvillier
Lee, A. (1999). CorporateMetrics – The Benchmark for Corporate RiskManagement. New
York: RiskMetrics Group
Rothengatter, W., & Schaffer, A. (2008): Makro kompakt – Grundzüge der Makroökonomik.
Heidelberg: Physica – Verlag
Seese, D., & Siebert, L., & Vogel, A. (2011). Risikomanagement durch Modellierung eines
makroökonomischen Marktmodells im Kontext unternehmensweiter Stresstests.
Risikomanager 15/2011
Seese, D., & Schlottmann, F., & Vogel, A. (2011). Market modelling for anticipating risk in a
context of macroeconomic stresstest. Proceedings of International Business Research
Conference. Dubai
Siebert, L. (2010). Modellierung eines makroökonomischen Modells: Bachelor Thesis,
Karlsruhe Institut für Technologie (KIT), Karlsruhe, Germany
Spremann, K., & Gantenbein, P. (2007). Zinsen, Anleihen, Kredite (4th ed.). München:
Oldenbourg
Stein, J., & Usher, S. E., & LaGatutta, D., & Youngen, J. (2001). A Comparables Approach
To Measuring Cash-Flow-at-Risk for Non-Financial Firms. Journal of Applied
Corporate Finance, 13(4)
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2012 Cambridge Business & Economics Conference
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Thome, H. (2005). Zeitreihenanalyse: eine Einführung für Sozialwissenschaftler und
Historiker. München: Oldenbourg Wissenschaftsverlag
Turner, C. (1996). VaR as an industrial tool. Risk, 9(3)
Veith, J. (2006). Bewertung von Optionen unter der Coherent Market Hypothesis.
Wiesbaden:Deutscher Universitats-Verlag - GWV Fachverlage GmbH
i
The developed model is an enhancement. For further details see also Seese, Siebert, Vogel (2011) or Seese,
Schlottmann, Vogel (2011)
ii
Income and price elasticity need to be estimated by internal research processes. They are individual and
depend on the company’s products.
iii
See Veith (2006)
iv
Those parameters turned out to be the most relevant market drivers of the company having a closer look at for
sample reasons
v
See http://www.destatis.de
vi
See Rothengatter, Schaffner (2008):
vii
See http://www.bundesbank.de
viii
See Junius, Kater, Meier, Müller (2002)
ix
See Spremann, Gantenbein (2007)
x
See http://www.destatis.de/jetspeed/portal/cms/Sites/destatis/Internet/DE/Presse/abisz/VPI,
templateId=renderPrint.psml
xi
See Lang (2005)
xii
See Backhaus, Erichson, Plinke, Weiber (2008)
xiii
See Backhaus, Erichson, Plinke, Weiber (2008)
xiv
See Thome (2005)
xv
See Veith (2006)
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